Finite element modeling of high-pressure deformation and phase transformation of silicon beneath a sharp indenter

Stress induced phase transitions in silicon

“…The few dedicated constitutive models published to this day Zhang, 2003, 2004;Kiriyama et al, 2009) do not adequately reproduce the experimental findings using a set of reasonable material parameters, nor are they set up in an appropriate finite deformation framework. Further, no attempt has been made to verify the models' predictions by comparison to experimental data that was not used for fitting the material parameters.…”

“…Further, the transformation threshold under hydrostatic loading was fitted to be 10 GPa, which is 13% lower than the experimental value of 11.3 GPa, and the indentation simulation overestimates the depth of the transformation zone by ∼ 70% (Vodenitcharova and Zhang, 2003). In a recent attempt Kiriyama et al (2009) used a multilinear "elastic" model with different tangent moduli for loading and unloading in order to fit the experimental load -displacement hysteresis. Such a model is neither capable of capturing the effect of triaxiality on the phase transition nor the independent evolution of volumetric and deviatoric inelastic strains.…”

Randomness and Statistical Laws of Indentation-Induced Pop-Out in Single Crystal Silicon

“…Research on single crystal silicon under external loads has been given much attention [1,2,3,4,5]. Nanoindentation as a powerful method to characterize properties of materials in micro/nano scale also has been used to study mechanical response of single crystal silicon under the penetration load [6,7,8,9,10,11,12,13,14,15,16]. …”

“…Unlike general materials which have smooth load-depth curves, discontinuities in the unloading curves named pop-out and elbow were observed during indentation testing of single crystal silicon [7,10,12,13,14,15,16], which responded to phase transformations of silicon beneath the indenter. Results of Raman microspectroscopy analysis of nanoindentations indicate that pop-out corresponds to the formation of Si–XII and Si–III phases [17], and elbow resulted from the amorphization of silicon on pressure release [13,14,16,17].…”

In situ observations of Berkovich indentation induced phase transitions in crystalline silicon films

“…This grouping of peaks is similar to the spectral profile of bc8 and r8[23–26] rather than β-tin (or Imma, sh)[27] observed during compression in DAC tests [1] and postulated to form on indentation loading. [3,28] To verify that the r8 and bc8 modes originate from the center of the contact and not from extruded and phase transformed material at the contact periphery,[29,30] the spatial distribution of these modes in the contact region was visualized by mapping the intensity of the strongest peak (P1). Figure 1(c) is an overlay of a grey scale plot of the intensity of that peak and a colored contour plot of the relative Raman shift of the LO-dc2 peak.…”